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(CNN) -- Major League Baseball is set to suspend some 20 players in the coming weeks due to a scandal involving performance-enhancing drugs, according to an ESPN report.

The network says it is potentially the worst drug abuse case in the history of baseball.

The league declined to comment to CNN, but confirmed that an investigation is in the works.

Baseball's highest-paid player, New York Yankee Alex "A-Rod" Rodriguez, as well as Ryan Braun of the Milwaukee Brewers are among those facing suspension, ESPN said, citing unnamed sources.

Both have denied using performance-enhancing drugs, or PEDs.

The league may seek to double the possible suspension time for affected players by counting the doping itself as one infraction and lying about having taken the drugs as a second one, ESPN reported.

Braun has faced suspension before, for a period of 50 games.

In 2012, a drug test showed high levels of testosterone in his body, but the outfielder successfully disputed the testing process, and the suspension was overturned in February.

Braun declined to comment on the ESPN report late Tuesday, but said he was sticking by his previous account. "The truth has not changed," he told reporters.

A Florida newspaper first leveled doping allegations at Rodriguez in January. The Miami New Times reported that the shortstop and third baseman had acquired the drugs from a Miami anti-aging clinic called "Biogenesis," run by Anthony Bosch.

ESPN said Bosch, who allegedly supplied baseball players with performance-enhancing substances, has agreed to cooperate in the MLB investigation.

Records obtained by MLB name many players, but league investigators need Bosch to attest to their accuracy and confirm that players were doping, ESPN reported, citing unnamed sources.

The league filed a suit against Biogenesis in March for allegedly supplying PEDs to players and advising them on how to avoid detection during drug tests.

ESPN reported that MLB may drop the suit against Bosch, if he cooperates in its investigation.

Managers tight-lipped

On Tuesday, the managers for the Yankees and the Brewers said little.

"I know Major League Baseball is handling it, and that's all I know," Brewers manager Ron Roenicke told journalists at a post-game news conference in Milwaukee.

Yankees manager Joe Girardi started out dodging reporters who grilled him on ESPN's report at a post-game news conference, but softened when it came to his concerns about Rodriguez.